Question

The sum of two numbers is $15$ and the difference of their squares is $15$. The difference of the numbers is __________.

• A. $0$
• B. $1$
• C. $4$
• D. $6$

Answer 1

The correct option is B $1$

Let the two numbers be $a$ and $b$

Thus $(a+b)=15$ ....(given)
and $(a^2-b^2)=15$ ....(given)

$\Rightarrow (a+b)(a-b)=15$

$\Rightarrow 15(a-b)=15$

$\Rightarrow (a-b)=1$ (difference of the numbers)